On the construction of operator-valued measures with projector-valued densities

Positive operator-valued measures play an important role in noncommutative probability theory. To construct them, it is convenient to consider the orbits of an irreducible projective unitary representation of some locally compact group. The resulting measure will be covariant with respect to the representation under consideration. Nevertheless, the construction of measures that are not covariant is of particular interest. The report will discuss both tasks and ways to solve them.